Being and event

Title ......Page 3
Copyright ......Page 4
Contents ......Page 5
Author\'s Preface ......Page 11
Translator\'s Preface ......Page 17
Introduction ......Page 35
Part I. Being: Multiple and Void. Plato/Cantor ......Page 55
1 The One and the Multiple: a priori conditions of any possible ontology ......Page 57
2 Plato ......Page 65
3 Theory of the Pure Multiple: paradoxes and critical decision ......Page 72
Technical Note: the conventions of writing ......Page 83
4 The Void: Proper name of being ......Page 86
1 The same and the other: the axiom of extensionality ......Page 94
2 The operations under condition: axioms of the powerset, of union, of separation and of replacement ......Page 96
3 The void, subtractive suture to being ......Page 100
6 Aristotle ......Page 104
Part II. Being: Excess, State of the Situation, One/Multiple, Whole/Parts, or E/C? ......Page 113
1 Belonging and inclusion ......Page 115
2 The theorem of the point of excess ......Page 118
3 The void and the excess ......Page 120
4 One, count-as-one, unicity, and forming-into-one ......Page 123
8 The State, or Metastructure, and the Typology of Being (normality, singularity, excrescence) ......Page 127
9 The State of the Historico-social Situation ......Page 138
10 Spinoza ......Page 146
Part III. Being: Nature and Infinity. Heidegger/Galileo ......Page 155
11 Nature: Poem or matheme? ......Page 157
1 The concept of normality: transitive sets ......Page 164
2 Natural multiples: ordinals ......Page 166
3 The play of presentation in natural multiples or ordinals ......Page 168
4 Ultimate natural element (unique atom) ......Page 172
5 An ordinal is the number of that of which it is the name ......Page 173
6 Nature does not exist ......Page 174
13 Infinity: the other, the rule and the Other ......Page 176
14 The Ontological Decision: \'There is some infinity in natural multiples\' ......Page 184
1 Point of being and operator of passage ......Page 185
2 Succession and limit ......Page 188
4 Infinity finally defined ......Page 190
5 The finite, in second place ......Page 193
1 The Matheme of infinity revisited ......Page 195
2 How can an infinity be bad? ......Page 198
3 The return and the nomination ......Page 199
4 The arcana of quantity ......Page 201
5 Disjunction ......Page 203
Part IV. The Event: History and Ultra-one ......Page 205
16 Evental Sites and Historical Situations ......Page 207
17 The Matheme of the Event ......Page 212
1 The ontological schema of historicity and instability ......Page 218
2 The axiom of foundation ......Page 219
4 Nature and history ......Page 221
5 The event belongs to that-which-is-not-being-qua-being ......Page 223
19 Mallarme ......Page 225
Part V. The Event: Intervention and Fidelity. Pascal/Choice; Holderlin/Deduction ......Page 233
20 The Intervention: Illegal choice of a name for the event, logic of the two, temporal foundation ......Page 235
21 Pascal ......Page 246
22 The Form-multiple of Intervention: is there a being of choice? ......Page 257
23 Fidelity, Connection ......Page 266
24 Deduction as Operator of Ontological Fidelity ......Page 274
1 The formal concept of deduction ......Page 276
2 Reasoning via hypothesis ......Page 278
3 Reasoning via the absurd ......Page 281
4 Triple determination of deductive fidelity ......Page 286
25 Holderlin ......Page 289
Part VI. Quantity and Knowledge. The Discernible (or Constructible): Leibniz/Godel ......Page 297
26 The Concept of Quantity and the Impasse of Ontology ......Page 299
1 The quantitative comparison of infinite sets ......Page 301
2 Natural quantitative correlate of a multiple: cardinality and cardinals ......Page 303
3 The problem of infinite cardinals ......Page 306
4 The state of a situation is quantitatively larger than the situation itself ......Page 307
5 First examination of Cantor\'s theorem: the measuring scale of infinite multiples, or the sequence of alephs ......Page 309
6 Second examination of Cantor\'s theorem: what measure for excess? ......Page 311
7 Complete errancy of the state of a situation: Easton\'s theorem ......Page 313
27 Ontological Destiny of Orientation in Thought ......Page 315
28 Constructivist Thought and the Knowledge of Being ......Page 320
29 The Folding of Being and the Sovereignty of Language ......Page 329
1 Construction of the concept of constructible set ......Page 330
2 The hypothesis of constructibility ......Page 333
3 Absoluteness ......Page 336
4 The absolute non-being of the event ......Page 338
5 The legalization of intervention ......Page 339
6 The normalization of excess ......Page 341
7 Scholarly ascesis and its limitation ......Page 343
30 Leibniz ......Page 349
Part VII. The Generic: Indiscernible and Truth. The Event — P.J. Cohen ......Page 359
31 The Thought of the Generic and Being in Truth ......Page 361
1 Knowledge revisited ......Page 362
2 Enquiries ......Page 363
3 Truth and veridicity ......Page 365
4 The generic procedure ......Page 369
5 The generic is the being-multiple of a truth ......Page 372
6 Do truths exist? ......Page 373
32 Rousseau ......Page 378
33 The Matheme of the Indiscernible: P.J. Cohen\'s strategy ......Page 389
1 Fundamental quasi-complete situation ......Page 392
2 The conditions: material and sense ......Page 396
3 Correct subset (or part) of the set of conditions ......Page 399
4 Indiscernible or generic subset ......Page 401
1 In danger of inexistence ......Page 406
2 Ontological coup de theatre: the indiscernible exists ......Page 407
3 The nomination of the indiscernible ......Page 410
4 $-referent of a name and extension by the indiscernible ......Page 412
5 The fundamental situation is a part of any generic extension, and the indiscernible $ is an element of any generic extension ......Page 415
6 Exploration of the generic extension ......Page 418
7 Intrinsic or in-situation indiscernibility ......Page 420
Part VIII. Forcing: Truth and the Subject. Beyond Lacan ......Page 423
35 Theory of the Subject ......Page 425
1 Subjectivization: intervention and operator of faithful connection ......Page 426
2 Chance, from which any truth is woven, is the matter of the subject ......Page 428
3 Subject and truth: indiscernibility and nomination ......Page 430
4 Veracity and truth from the standpoint of the faithful procedure: forcing ......Page 434
5 Subjective production: decision of an undecidable, disqualification, principle of inexistents ......Page 440
36 Forcing: from the indiscernible to the undecidable ......Page 444
1 The technique of forcing ......Page 446
2 A generic extension of a quasi-complete situation is also itself quasi-complete ......Page 450
3 Status of veridical statements within a generic extension S($): the undecidable ......Page 451
4 Errancy of excess (1) ......Page 454
5 Absenting and maintenance of intrinsic quantity ......Page 457
6 Errancy of excess (2) ......Page 459
7 From the indiscernible to the undecidable ......Page 460
37 Descartes/Lacan ......Page 465
Appendixes ......Page 473
1 Principle of minimality for ordinals ......Page 475
2 A relation, or a function, is solely a pure multiple ......Page 477
3 Heterogeneity of the cardinals: regularity and singularity ......Page 482
4 Every ordinal is constructible ......Page 487
5 On absoluteness ......Page 490
6 Primitive signs of logic and recurrence on the length of formulas ......Page 493
7 Forcing of equality for names of the nominal rank 0 ......Page 496
8 Every generic extension of a quasi-complete situation is itself quasi-complete ......Page 501
9 Completion of the demonstration of |p(w0)|>d within a generic extension ......Page 505
10 Absenting of a cardinal d of S in a generic extension ......Page 507
11 Necessary condition for a cardinal to be absented in a generic extension ......Page 509
12 Cardinality of the antichains of conditions ......Page 511
Notes ......Page 515
Dictionary ......Page 532